Steven Pulos

Proportional Reasoning: A Review of the Literature.

This paper presents a review of the research on proportional reasoning. Methodologies used in proportional reasoning studies are presented first. The discussion is then organized around the following topics: strategies use to solve proportion problems, including erroneous strategies; factors that influence performance on proportion problems, both task-related and subject-related; training studies. The discussion is accompanied by suggestions for educational and research applications.

Early Adolescents' Proportional Reasoning on 'Rate' Problems.

The study deals with qualitative features of proportional reasoning on dimensional intensive variables by eleven and thirteen year-old students. These features include types of comparison and types of strategies employed. Four proportional problems, varying in numerical and referential content were administered to 116 eleven year-olds and 137 thirteen year-olds. No significant age effect was found. The relative frequencies with which the type of comparison and various strategies were used was greatly affected by context, numerical content of the problem, and the immediately preceeding task. No type of comparison appeared to be more ‘natural’ than another, as suggested in previous research.

How Therapy is Conducted in the Private Consulting Room: A Multidimensional Description of Brief Psychodynamic Treatments

Thirty patients representing a range of neurotic disorders were treated in a brief, 16-session psychodynamic psychotherapy in private practice settings. Verbatim transcripts of therapy hours were rated by judges with the Psychotherapy Process Q-set, designed to provide a standard language for the description and classification of therapy process. The sample demonstrated statistically significant change pre- to posttreatment, and a majority of patients met at least one criterion for clinically significant change. A longitudinal view of the process suggests that these treatments were characterized by what could be described as a gradual shift from an external, reality-oriented construction of personal difficulties to an emphasis on inner experience and the relationship with the therapist. Results are framed within a conceptualization of process as actions that define and give meaning to one another and their context. It is argued that such a conceptualization more adequately captures clinical realities and ...

Modification of Gender Differences in the Understanding of Displaced Volume

Males generally perform better than females on tasks involving the displaced-volume concept. This training study examined whether experience and/or aptitudes play parts in this differential performance. Middleclass 8th graders who failed items on a group pre-test of displaced volume were assigned to training or control groups. All trained subjects, male or female, improved in performance on the displaced-volume task. Observations of facial expressions and postures during training added to evidence that males and females responded similarly to training. The control group showed gains as well. Training effects did not generalize to related tasks. Improvement during training was related to an aspect of Field Dependence-Independence called Familiar Field.

Generality of Proportional Reasoning in Early Adolescence: Content Effects and Individual Differences:

Two hundred forty eight adolescents from grades 6 and 8 were given a proportional reasoning task and a battery of eight cognitive style, ability, and attitude measures. The problems in the proportional reasoning task varied in referential content and numerical structure. The cognitive ability and style dimensions examined consisted of: Crystallized intelligence, fluid intelligence, field dependency, divergent thinking, visualization ability, and M capacity. An age x sex x content x structure ANOVA found a significant main effect only for numerical structure. A significant age x sex x content interaction was also found. A simultaneous model multiple regression found a significant effect for only fluid ability, M capacity, and divergent thinking when the other variables were held constant.

Setting Effects in Mathematical Reasoning of Early Adolescents: Findings from Three Urban Schools

Three mathematical reasoning tasks (proportions, reasoning with an unknown, and a spatial reasoning task), and an attitude interview were individually administered to 260 8th grade students from three predominately minority urban schools. The three schools and neighborhoods varied in educational advantages as well as in socioeconomic characteristics. An additional 60 students, from a middle class and predominately white school in which a similar study had been conducted previously, was included in some comparisons. A battery of groupadministered cognitive tasks and attitude scales was also administered to the students. The results showed a significant effect for site on all three tasks; however, the variance accounted for by site was slight for the spatial reasoning task and reasoning with unknowns (approximately 5%) while it was substantially larger for porportions (21%). Other characteristics that differed across sites were: (a) solution strategies for reasoning with unknowns and in the simple proportion problems; (b) cognitive correlates for each task; and (c) attitude regarding perceived competence and need for mathematics as well as for the perceived amount of effort expended on mathematics. The results are interpreted to indicate the need for an ecological approach to research on adolescent reasoning. Multiple tasks should be examined in multiple settings, and the relationship between attitudes and cognition should be considered.